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holomorphic germ

Germ (mathematics) — In mathematics, the notion of a germ of an object in/on a topological space captures the local properties of the object. In particular, the objects in question are mostly functions (or maps) and subsets. In specific implementations of this idea,… … Wikipedia
Milnor number — In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex valued holomorphic function germ then the Milnor number of f, denoted μ(f), is either an… … Wikipedia
Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… … Wikipedia
Exponential sheaf sequence — In mathematics, the exponential sheaf sequence is a fundamental short exact sequence of sheaves used in complex geometry.Let M be a complex manifold, and write O M for the sheaf of holomorphic functions on M . Let O M * be the subsheaf consisting … Wikipedia
Analytic continuation — In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where … Wikipedia